It is known to use catalytic systems based on halogenated metallocene complexes of lanthanides for copolymerizing ethylene and a conjugated diene.
The document EP-A-1 092 731 teaches the use, in producing copolymers of ethylene and a conjugated diene, of a catalytic system comprising:                on the one hand, an organometallic complex represented by one of the following generic formulae A or B:        

where Ln represents a lanthanide metal having an atomic number which can range from 57 to 71,
where X represents a halogen which can be chlorine, fluorine, bromine or iodine,
where Cp1 and Cp1 each comprise a cyclopentadienyl or fluorenyl group which is substituted or unsubstituted and where P is a bridge corresponding to the formula MR1R2, where M is an element from Group IVa of the Periodic Table of the Elements and where R1 and R2 represent an alkyl group comprising from 1 to 20 carbon atoms, and                on the other hand, a cocatalyst which is chosen from a group consisting of an alkylmagnesium, alkyllithium, alkylaluminium, and a Grignard reagent or which is composed of a mixture of these constituents.        
The document Patent WO-A-2004/035639 on behalf of the Applicants teaches the use, in producing copolymers of ethylene and butadiene, of a catalytic system comprising:
(i) a lanthanide metallocene complex represented by one or other of the following formulae:

where Ln represents a lanthanide metal having an atomic number which can range from 57 to 71,
where X represents a halogen which can be chlorine, fluorine, bromine or iodine,
where, in the first formula, two identical or different ligand molecules Cp1 and Cp2, each composed of a fluorenyl group which is substituted or unsubstituted, are connected to the said metal Ln, and
where, in the second formula, a ligand molecule composed of two identical or different fluorenyl groups Cp1 and Cp2 which are substituted or unsubstituted and which are connected to one another via a bridge P corresponding to the formula MR1R2, where M is an element from Group IVa of the Periodic Table of the Elements and where R1 and R2 represent an alkyl group comprising from 1 to 20 carbon atoms, is connected to the said metal Ln, and
(ii) a cocatalyst belonging to the group consisting of an alkylmagnesium, an alkyllithium, an alkylaluminium, and a Grignard reagent or which is composed of a mixture of these constituents.
Other catalytic systems based on monocyclopentadienyl complexes of lanthanide borohydride type are known in particular in the literature for the homopolymerization of diolefins.
Mention may be made, for example, of the paper by D. Barbier-Baudry, O. Blacque, A. Hafid, A. Nyassi, H. Sitzmann and M. Visseaux, European Journal of Inorganic Chemistry 2000, 2333-2336, which mentions a complex of formula (C5H(iPr)4)Ln(BH4)2(THF) including a monocyclopentadienyl ligand substituted by an isopropyl group (iPr), where THF is tetrahydrofuran, for the homopolymerization of isoprene or styrene after alkylation by a cocatalyst of organolithium type.
More recently, the paper by F. Bonnet, M. Visseaux, A. Pereira and D. Barbier-Baudry, Macromolecules, 2005, 38, 3162-3169, disclosed the use of a similar complex of formula (C5Me4(nPr))Nd(BH4)2(THF)2 including a pentasubstituted monocyclopentadienyl ligand, where nPr is an n-propyl group, in the stereospecific 1,4-trans polymerization of isoprene after alkylation by a cocatalyst of dialkylmagnesium type.
It should be noted that these lanthanide borohydride monocyclopentadienyl complexes have not been used to date in the copolymerization of monoolefins and conjugated dienes.
The Chinese patent document 1 286 256 discloses, as polymerization catalysts for the synthesis of polymethacrylates, a borohydride metallocene complex of a lanthanide comprising a ligand molecule composed of a fluorenyl group corresponding to the following formula:{[(X1)2(R7)(C5R1R2R3R4)(C13H6R5R6)]MX2(L)n}m,where:
X1 represents an alkyl group having from 1 to 4 carbon atoms or a phenyl group,
X2 represents Cl, BH4, H, an alkyl group having from 1 to 4 carbon atoms, N[Si(CH3)3]2, CH2[Si(CH3)3] or tetrahydrofuran,
R1, R3 and R4 represent H or the CH3 radical,
R2 represents H,
R5 and R6 represent H, an alkyl group having from 1 to 4 carbon atoms or Si(CH3)3,
R7 represents Si, C, Ge or Sn,
M represents a lanthanide, yttrium or scandium,
L represents Si(CH3)3, Li(THF)4, [crown ether Y] or [crown ether Y]-2,4-epoxyhexacycle,
n represents 0 or 1 and m=1 or 2 (if m=2, n=0),
Y is a monovalent metal.
Another recent research route has concerned borohydride metallocene complexes of lanthanides including a ligand based on two cyclopentadienyl groups. Mention may be made, for example, of the studies by S. M. Cendrowski-Guillaume et al., Organometallics, 2000, 19, 5654-5660, and Macromolecules, 2003, 36, 54-60, which have disclosed the use of such a metallocene complex, of formula (C5Me5)2Sm(BH4)(THF), where Me is a methyl group and where Sm is samarium, for specifically catalysing the polymerization of ε-caprolactone by ring opening.
Mention may also be made of the studies by M. Visseaux et al., Journal of Organometallic Chemistry, 691 (2006), pages 86-92, which have disclosed that the metallocene Cp*2Nd(BH4)(THF), when it is used in combination with butylethylmagnesium, even in the presence of a large excess of THF, constitutes a very active catalyst for ethylene and, in the presence of a stoichiometric amount of butylethylmagnesium, makes possible the stereospecific 1,4-trans polymerization of isoprene.